American Airlines said Straka was asked five times in all, before being deplaned.
The Boeing 737 service to Dallas then departed without Straka, four minutes behind schedule.
Straka, a former hairdresser turned conservative commentator, proceeded to make his case online for not wearing a mask.
"They're currently trying to rebook me. They told me I MUST wear a mask on my next flight. STILL nobody has asked if there's a reason why I can't," he wrote.
Straka said it was the airline's "mistake" for deplaning him and that they were wrong to tell him it was a legal requirement to wear the face covering.
In a video recording, shared via the Periscope app, Straka claimed he was intimidated into leaving the plane and was never asked if there was a medical reason why he could not comply with the requirement. However, this claim was later disproven.
A journalist who was flying on the same service recorded the incident, in which he was clearly asked if he had a doctor's note.
Astead Herndon, a reporter for the New York Times and CNN, shared audio from the cabin in which staff could be heard telling Straka that: if he had a medical condition he "wouldn't have had to wear his mask for check in."
In the audio, a woman can be overhead shouting: "Sir, can you put it on or get off?"
"Brandon Straka declined to wear a face covering," the American Airlines said in a statement. "After he refused to comply with the instructions provided by the flight crew, our team members asked him to deplane.
"Mr. Straka stated to our airport team members that he would comply with our policies, and was rebooked on a later flight."
The airline offered to reroute the passenger onto a later service but was refused board, after again removing his mask.